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Magnetism of the spin-$\frac12$ $\alpha$-KVOPO$_4$ is studied bythermodynamic measurements, $^{31}$P nuclear magnetic resonance (NMR), neutrondiffraction, and density-functional band-structure calculations. FerromagneticCurie-Weiss temperature of $\theta_{\rm CW}\simeq 15.9$ K and the saturationfield of $\mu_0H_s\simeq 11.3$ T suggest the predominant ferromagnetic couplingaugmented by a weaker antiferromagnetic exchange that leads to a short-rangeorder below 5 K and the long-range antiferromagnetic order below $T_{\rmN}\simeq 2.7$ K in zero field. Magnetic structure with the propagation vector$\mathbf k=(0,\frac12,0)$ and the ordered magnetic moment of 0.58 $\mu_B$ at1.5 K exposes a non-trivial spin lattice where strong ferromagnetic dimers arecoupled antiferromagnetically. The reduction in the ordered magnetic momentwith respect to the classical value (1 $\mu_{\rm B}$) indicates sizable quantumfluctuations in this setting, despite the predominance of ferromagneticexchange. We interpret this tendency toward ferromagnetism as arising from theeffective orbital order in the folded chains of the VO$_6$ octahedra.

Quantum magnetism of ferromagnetic spin dimers in $\alpha$-KVOPO$_4$